The nonlinear-by-singularity systems

Abstract

The present work focuses on singularities, in terms of time functions, which are met in description of switching or sampling electronics systems, and on understanding of some basic nonlinear physical systems. The state-form dx/dt = [A(x,t)]x + [B(x,t)]u(t), and not the normal-form dx/dt = Phi(x,u,t), is preferred for use. The possibility of the state-variables appearing in the matrices in a singular system is considered in parallel with the possibility that the nonlinearity of a system will be directly seen by a designer.